Secure Computation Device, Comparison Method, Comparison Program Recording Medium, and Secure Computation System

1. A secure computation device for use in each of three secure computation devices which share and save, as three shared values, data to be kept secret, each of the three secure computation devices carrying out secret sharing which is classified into bit sharing and ring sharing, the data being represented in the bit sharing by an exclusive OR of the three shared values, the data being represented in the ring sharing by an addition on the ring of the three shared values, the secure computation device comparing, in a case where a first integer a and a second integer b, each of which is more than 0 and less than 2{circumflex over ( )}k (where k is an integer equal to or more than one), are subjected to the ring sharing, the first integer a with the second integer b, wherein the secure computation device comprises: an addition/subtraction circuitry configured to carry out a predetermined addition/subtraction using the first integer a, the second integer b, and 2{circumflex over ( )}k with the ring sharing to produce an added/subtracted result; a bit decomposition circuitry configured to convert the added/subtracted result with the bit sharing to produce a bit shared result; and a bit extraction circuitry configured to extract a (k+1)-th bit of the bit shared result to produce an extracted result.

2. The secure computation device as claimed in claim 1 , wherein the bit extraction circuitry comprises a shifting circuitry configured to shift the bit shared result right by k bits to produce a shifted result as the extracted result.

3. The secure computation device as claimed in claim 2 , further comprising a bit composition circuitry configured to convert the shifted result with the ring sharing to produce a ring shared result.

4. The secure computation device as claimed in claim 1 , wherein: in a case of detecting whether or not the first integer a is not more than the second integer b, the addition/subtraction circuitry is configured to calculate (b+2{circumflex over ( )}k−a) with the ring sharing as the predetermined addition/subtraction to produce (b+2{circumflex over ( )}k−a) as the added/subtracted result.

5. The secure computation device as claimed in claim 1 , wherein: in a case of detecting whether or not the first integer a is less than the second integer b, the addition/subtraction circuitry is configured to calculate (b+2{circumflex over ( )}k−(a+1)) with the ring sharing as the predetermined addition/subtraction to produce (b+2{circumflex over ( )}k−(a+1)) as the added/subtracted result.

6. The secure computation device as claimed in claim 1 , wherein: in a case of detecting whether or not the first integer a is not less than the second integer b, the addition/subtraction circuitry is configured to calculate (a+2{circumflex over ( )}k−b) with the ring sharing as the predetermined addition/subtraction to produce (a+2{circumflex over ( )}k−b) as the added/subtracted result.

7. The secure computation device as claimed in claim 1 , wherein: in a case of detecting whether or not the first integer a is more than the second integer b, the addition/subtraction circuitry is configured to calculate (a+2{circumflex over ( )}k−(b+1)) with the ring sharing as the predetermined addition/subtraction to produce (a+2{circumflex over ( )}k−(b+1)) as the added/subtracted result.

8. A secure computation system comprising N secure computation devices each of which is described in claim 1 , where N represents an integer which is not less three.

9. A comparison method for use in each of three secure computation devices which share and save, as three shared values, data to be kept secret, each of the three secure computation devices carrying out secret sharing which is classified into bit sharing and ring sharing, the data being represented in the bit sharing by an exclusive OR of the three shared values, the data being represented in the ring sharing by an addition on the ring of the three shared values, the comparison method comparing, in a case where a first integer a and a second integer b, each of which is more than 0 and less than 2{circumflex over ( )}k (where k is an integer equal to or more than one), are subjected to the ring sharing, the first integer a with the second integer b in a secure computation device, wherein the comparison method comprises: an addition/subtraction step of carrying out a predetermined addition/subtraction using the first integer a, the second integer b, and 2{circumflex over ( )}k with the ring sharing to produce an added/subtracted result; a bit decomposition step of converting the added/subtracted result with the bit sharing to produce a bit shared result; and a bit extraction step of extracting a (k+1)-th bit of the bit shared result to produce an extracted result.

10. The comparison method as claimed in claim 9 , wherein the bit extraction step comprises a shifting step of shifting the bit shared result right by k bits.

11. The comparison method as claimed in claim 9 , wherein: in a case of detecting whether or not the first integer a is not more than the second integer b, the addition/subtraction step calculates (b+2{circumflex over ( )}k−a) with the ring sharing as the predetermined addition/subtraction to produce (b+2{circumflex over ( )}k−a) as the added/subtracted result.

12. The comparison method as claimed in claim 9 , wherein: in a case of detecting whether or not the first integer a is less than the second integer b, the addition/subtraction step calculates (b+2{circumflex over ( )}k−(a+1)) with the ring sharing as the predetermined addition/subtraction to produce (b+2{circumflex over ( )}k−(a+1)) as the added/subtracted result.

13. The comparison method as claimed in claim 9 , wherein: in a case of detecting whether or not the first integer a is not less than the second integer b, the addition/subtraction step calculates (a+2{circumflex over ( )}k−b) with the ring sharing as the predetermined addition/subtraction to produce (a+2{circumflex over ( )}k−b) as the added/subtracted result.

14. The comparison method as claimed in claim 9 , wherein: in a case of detecting whether or not the first integer a is more than the second integer b, the addition/subtraction step calculates (a+2{circumflex over ( )}k−(b+1)) with the ring sharing as the predetermined addition/subtraction to produce (a+2{circumflex over ( )}k−(b+1)) as the added/subtracted result.

15. A non-transitory computer readable recording medium storing a comparison program for use in each of three secure computation devices which share and save, as three shared values, data to be kept secret, each of the three secure computation devices carrying out secret sharing which is classified into bit sharing and ring sharing, the data being represented in the bit sharing by an exclusive OR of the three shared values, the data being represented in the ring sharing by an addition on the ring of the three shared values, the comparison program causing, in a case where a first integer a and a second integer b, each of which is more than 0 and less than 2{circumflex over ( )}k (where k is an integer equal to or more than one), are subjected to the ring sharing, a computer serving as a secure computation device to compare the first integer a with the second integer b, wherein the comparison program causes the computer to achieve: an addition/subtraction function of carrying out a predetermined addition/subtraction using the first integer a, the second integer b, and 2{circumflex over ( )}k with the ring sharing to produce an added/subtracted result; a bit decomposition function of converting the added/subtracted result with the bit sharing to produce a bit shared result; and a bit extraction function of extracting a (k+1)-th bit of the bit shared result to produce an extracted result.

16. The non-transitory computer readable recording medium as claimed in claim 15 , wherein the bit extraction function comprises a shifting function of shifting the bit shared result right by k bits.

17. The non-transitory computer readable recording medium as claimed in claim 15 , wherein: in a case of detecting whether or not the first integer a is not more than the second integer b, the addition/subtraction function calculates (b+2{circumflex over ( )}k−a) with the ring sharing as the predetermined addition/subtraction to produce (b+2{circumflex over ( )}k−a) as the added/subtracted result.

18. The non-transitory computer readable recording medium as claimed in claim 15 , wherein: in a case of detecting whether or not the first integer a is less than the second integer b, the addition/subtraction function calculates (b+2{circumflex over ( )}k−(a+1)) with the ring sharing as the predetermined addition/subtraction to produce (b+2{circumflex over ( )}k−(a+1)) as the added/subtracted result.

19. The non-transitory computer readable recording medium as claimed in claim 15 , wherein: in a case of detecting whether or not the first integer a is not less than the second integer b, the addition/subtraction function calculates (a+2{circumflex over ( )}k−b) with the ring sharing as the predetermined addition/subtraction to produce (a+2−k−b) as the added/subtracted result.

20. The non-transitory computer readable recording medium as claimed in claim 15 , wherein: in a case of detecting whether or not the first integer a is more than the second integer b, the addition/subtraction function calculates (a+2−k−(b+1)) with the ring sharing as the predetermined addition/subtraction to produce (a+2−k−(b+1)) as the added/subtracted result.